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<h1 align="center">F<sub>max</sub> Normalization</h1>

<p>Fmax normalization corrects for well-to-well differences in the fluorescence 
scale generated by the instrument's optical system. Because LRE quantification 
is founded upon determining target quantity expressed in fluorescence units, any 
variance in the fluorescence units generated by individual wells produces a 
corresponding error in target quantification, albeit in a linear fashion. </p>
<p>The LRE Analyzer provides an option to correct for such variances by 
adjusting target quantities relative to the average Fmax generated by all of the 
profiles within a run. This type of internal calibration also provides a quality 
control method for assessing both inter- and intra-run variances in 
fluorescence intensity. This is based on comparing the average Fmax across 
multiple runs and the average Fmax coefficient of variance generated within individual runs, respectively, 
values for which are provided within the 
run label.</p>
<p align="center">
<img border="0" src="images/fmax_normzn1.gif" width="442" height="144"></p>
<p>Fmax normalization is applied by selecting the &quot;Fmax Normalize&quot; checkbox 
located just above the explorer panel tree, while deselecting the checkbox 
removes Fmax normalization. An asterisk (*) is also added to the profile 
label to indicate that Fmax normalization has been applied. </p>
<p align="center">
<img border="0" src="images/fmax_normzn2.gif" width="411" height="134"></p>
<p align="left">Although such well-to-well differences are generally small, 
below 
is an extreme example in which a badly calibrated instrument generated up to 
1-fold difference in target quantity, as revealed by conducting 96 identical amplification reactions (1876 
lambda genomes + CAL1):</p>
<p align="center">
<img border="0" src="images/amp_plot.gif" width="447" height="310"></p>
<p align="left">The Fc plot within the profile editor panel presents the average 
Fmax as a line, to which individual profiles can be compared. These are two of 
the most extreme profiles, which generated close to a 1-fold difference in 
predicted target 
quantity:</p>
<p align="center">
<img border="0" src="images/fmax_normzn3.gif" width="361" height="318"></p>
<p align="center">
<img border="0" src="images/fmax_normzn4.gif" width="359" height="315"></p>
<p>Also worthy of note is that the C<sub>1/2</sub> values are nearly identical 
(as is the case for all of the other profiles within this run), whereas the 
corresponding Cq values difference by 1.0 cycle. </p>
<p>Although not formally 
documented, in the absence of other factors (however, see below), these 
differences in profile height likely reflect differences in the fluorescence 
scale generated by the instrument's optical system. </p>
<p>Fmax normalization compares a profile's Fmax to the run's average Fmax and 
adjusts the predicted target quantity based on their difference. For example, if 
a profile generates a Fmax that is 50% higher than the average Fmax, it will 
generate a 50% overestimation of target quantity. Fmax normalization corrects 
for this bias by simply lowering the predicted target quantity by 50%. If the 
profile Fmax is lower than the average, the predicted target quantity is 
similarly increased.</p>
<p><font color="#FF0000"><b>Some important qualifications</b></font><br>
Importantly, this approach assumes the absence of other factors impacting 
profile height, which is 
not necessarily the case. For example, differences in amplification efficiency 
(Emax) also impacts Fmax in a linear fashion
<a href="../lre_overview/lre_literature.html">(Rutledge and Stewart 2010)</a>. </p>
<p class="auto-style1"><a href="../lre_overview/lre_introduction.html">
<img alt="" class="auto-style2" height="51" src="../lre_overview/images/Fmax_equation.gif" width="103"></a></p>
<p>Thus, a necessary assumption of Fmax normalization as it is applied in this 
version of the LRE Analyzer, is that amplification efficiency is similar for all profiles within a run. 
However, note that even for samples that generate extremely low amplification 
efficiencies, the corresponding quantitative error produced by Fmax 
normalization is modest, and is linear in 
relation to the amplification efficiency difference. </p>
<p>For example, at 80% amplification efficiency target quantity will be 
overestimated by 20% when Fmax normalization is applied. This is in fact small in 
relation to the impact of errors in Emax determination, where a 20% 
overestimation of target quantity is roughly equivalent to a 1.5% 
underestimation of Emax. </p>
<p>Another underlying assumption of Fmax normalization is that all 
amplicons generate similar fluorescence intensities (FU/bp), which, as based on previous 
work <a href="../lre_overview/lre_literature.html">(Rutledge and Stewart 2010)</a>, 
appears to be generally valid. However, during implementation of Fmax 
normalization, rare exceptions to this assumption were revealed. </p>
<p>For example, the SAND F1R1 amplicon that is included in the demonstration 
experiment database, 
consistently generates Fmax values that are about 25% lower than the average 
Fmax of other amplicons. This in turn suggests that this amplicon generates a 25% lower 
fluorescence intensity, although this has not been been formally investigated. 
Worthy of note, it could be counter argued that Fmax normalization actually corrects for 
such putative amplicon-specific differences in fluorescence intensity.</p>

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